arXiv subjects

A. Matzkin

Publications and source records attributed to A. Matzkin.

At least 55 records · Page 3Linked to original sources

arXiv2012

Weak and semiweak values in non-ideal spin measurements: an exact treatment beyond the asymptotic regime

We consider weak measurements (WM) of a spin observable in quantum mechanics beyond the usual asymptotic regime. This is done by obtaining the exact time-dependent wave functions of the measuring apparatus for general non-ideal measurements. Ideal strong measurements and the usual WM regime are obtained as the two extreme limiting cases of our exact treatment. We show that in the intermediate regime non-ideal measurements lead to "semiweak" eccentric values that differ from the usual weak values. We further show that even in the WM regime the exact treatment leads to a meter behavior that can be markedly distinct from the one predicted by the usual WM formalism. We give several illustrations and discuss an application to the distinction of different realizations of the same density matrix.

quant-ph↗

arXiv2010

Communicating with a wave packet using quantum superarrival

An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (`superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence between the strength of the barrier and the magnitude of `superarrival'.

quant-ph↗

arXiv2009

Local models and EPR quantum correlations

A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's ``completeness or locality'' dilemma.

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arXiv2009

A local model violating Bell's inequalities

quant-ph↗

arXiv2009

A local scheme accounting for EPR quantum correlations

quant-ph↗

arXiv2009

Is Bell's theorem relevant to quantum mechanics? On locality and non-commuting observables

Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective of the issue of locality. Then, we try to disentangle the locality issue from the existence of joint distributions by introducing two models accounting for the EPR correlations but denying the existence of joint distributions. We will see that these models do not need to resort explicitly to non-locality: the first model relies on conservation laws for ensembles, and the second model on an equivalence class by which different configurations lead to the same physical predictions.

quant-ph↗

arXiv2008

Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.

quant-ph↗

arXiv2008

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.

quant-ph↗

arXiv2008

Classical statistical distributions can violate Bell-type inequalities

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.

quant-ph↗

arXiv2007

Quantum and semiclassical phase functions for the quantization of symmetric oscillators

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schrödinger equation. For anharmonic oscillators, first order semiclassical quantization is seldom accurate and the higher order expansions eventually break down given the asymptotic nature of the series. A quantum phase that allows in principle to retrieve the exact quantum mechanical quantization condition and wavefunctions is given along with an iterative scheme to compute it. The arbitrariness surrounding quantum phase functions is lifted by supplementing the phase with boundary conditions involving high order semiclassical expansions. This allows to extend the definition of oscillation numbers, that determine the quantization of the harmonic oscillator, to the anharmonic case. Several illustrations involving homogeneous as well as coupling constant dependant anharmonic oscillators are given.

quant-ph↗

arXiv2007

Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems

The de Broglie-Bohm interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned by the de Broglie-Bohm account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display the manifestation of classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have a regular or disordered aspect depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences on the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the de Broglie-Bohm motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems.

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arXiv2006

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' -- from the point of view of the de Broglie Bohm (BB) interpretation of quantum mechanics. The trajectories predicted by BB theory are computed and contrasted with the time evolution of the wavefunction, which shows pronounced features at times matching the period of closed orbits of the classical hydrogen in a magnetic field problem. Individual BB trajectories do not possess these periodicities and cannot account for the quantum recurrences. These recurrences can however be explained by BB theory by considering the ensemble of trajectories compatible with an initial statistical distribution, although none of the trajectories of the ensemble are periodic, rendering unclear the dynamical origin of the classical periodicities.

quant-ph↗

arXiv2006

Scattering induced dynamical entanglement and the quantum-classical correspondence

The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial revivals, which are expected to persist in the semiclassical limit, affect the long time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.

quant-ph↗

arXiv2006

Non-Hermitian quantum mechanics: the case of bound state scattering theory

Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a numerical example involving scattering by a short-range potential in a Coulomb field for which it is seen that even for a small but non-negligible non-Hermiticity index the non-Hermitian character of the problem must be taken into account. The computation of physical quantities in the relevant Hilbert spaces is also discussed.

quant-ph↗

arXiv2005

Rydberg wavepackets in terms of hidden-variables: de Broglie-Bohm trajectories

The dynamics of highly excited radial Rydberg wavepackets is analyzed in terms of de Broglie-Bohm (BB) trajectories. Although the wavepacket evolves along classical motion, the computed BB trajectories are markedly different from the classical dynamics: in particular none of the trajectories initially near the atomic core reach the outer turning point where the wavepacket localizes periodically. The reasons for this behavior, that we suggest to be generic for trajectory-based hidden variable theories, are discussed.

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arXiv2004

Exact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation

Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate results and eventually diverges due to the asymptotic nature of the expansion. A quantum phase is derived to bypass these shortcomings. It achieves exact quantization of nonsolvable potentials and allows to obtain the quantum wavefunction while locally approaching the best pre-divergent semiclassical expansion. An iterative procedure allowing to implement practical calculations with a modest computational cost is also given. The theory is illustrated on two examples for which the limitations of the semiclassical approach were recently highlighted: cold atomic collisions and anharmonic oscillators in the nonperturbative regime.

quant-ph↗

arXiv2003

Observation of diffractive orbits in the spectrum of excited NO in a magnetic field

We investigate the experimental spectra of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.

physics.atom-ph↗

arXiv2002

Realism and the wave-function

Realism -- the idea that the concepts in physical theories refer to 'things' existing in the real world -- is introduced as a tool to analyze the status of the wave-function. Although the physical entities are recognized by the existence of invariant quantities, examples from classical and quantum physics suggest that not all the theoretical terms refer to the entities: some terms refer to properties of the entities, and some terms have only an epistemic function. In particular, it is argued that the wave-function may be written in terms of classical non-referring and epistemic terms. The implications for realist interpretations of quantum mechanics and on the teaching of quantum physics are examined.

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